The single server queue in discrete time-numerical analysis I

1973 ◽  
Vol 20 (2) ◽  
pp. 297-304 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Numerical Analysis ◽  
Discrete Time ◽  
Single Server ◽  
Single Server Queue ◽  
Server Queue

The single-server queue with independent GI/G and M/G input streams

1987 ◽  
Vol 19 (1) ◽  
pp. 266-286 ◽  
Author(s):  
Teunis J. Ott
Keyword(s):  
Distribution Function ◽  
Numerical Analysis ◽  
Real Time ◽  
Queueing System ◽  
Single Server ◽  
Equivalent System ◽  
Single Server Queue ◽  
Input Stream ◽  
Server Queue ◽  
Single Input

This paper studies the single-server queueing system with two independent input streams: a GI/G and an M/G stream. A new proof is given of an old result which shows how this system can be transformed into an equivalent ‘single input stream’ GI/G/1 queue, and methods to study that equivalent system numerically are given. As part of the numerical analysis, algorithms are given to compute the moments and the distribution function of busy periods in the M/G/1 queue, and of other related busy periods. Special attention is given to the single-server queue with independent D/G and M/G input streams.This work is to be used in the modeling of real-time computer systems, which can often be described as a single-server queueing system with independent D/G and M/G input streams, see for example Ott (1984b).

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